Wireless-N laptop not working on 802.11g WiFi

I have a Dell laptop (Win7 Home Premium, 64Bit) and it seems like it always has difficulty connecting to WiFi routers that are using 802.11g. I have a Wireless-N card on my laptop and I would think it would be backwards compatible, right??
I'm the same person, with the same laptop, as this post: http://forums.techguy.org/networking/1079721-dns-lookup-failed.html
and all the symptoms that I was trying to solve in that post are relevant again.
At the time that post was made, I lived in an apartment and the modem/router from my cable company was wireless-G and my laptop seemed to experience intermittent DNS problems. I could never REALLY use the internet for very long, but sometimes some websites would seem to load, but usually pictures would have a problem. Other times the seemingly DNS issue would not let me load any websites at all. While I was on vacation I was able to connect perfectly to 2 different WiFi networks. I know for sure that one of them was Wireless-N (not sure about the other one).
Eventually I moved and my new modem/router from my new cable company was Wireless-N. My computer has connected to that network perfectly for months. Now, on vacation again, I tried to connect to a "G" network again and all the old problems came back EXACTLY as they were before.
Is it possible that my Wireless-N card has that much trouble connecting to Wireless-G networks? If so, is there any fix??
I've attached 2 screenshots. One is the Xirrus Wi-Fi Inspector showing my connection to the "G" network, the other is a shot of what Chrome looked like when it would not load the webpage.

Attached Files:

The signal is too weak for a reliable connection. Try closer to the router.

The variation in the signal strength indicates probable incorrect driver or defective adapter or router (or wireless access point). Try the latest wireless driver from the laptop manufacturer's web site. If that does not work right try the driver directly from Intel's site.

If possible check Xirrus with another computer, or another adapter, to see if the router is having difficulty maintaining a constant signal strength (a variation of one or two dBm is OK).

No, that's not the problem. I realize my signal was weak when I took that screenshot. I have another screenshot from just now (but can't post it because of the issue I'm trying to fix), the signal has been steady at about -57 dBm (ranging from about -55 to -59).